# Seminar on Reckoning

usually takes place Wednesday at 11:00 in Institute of Mathematics AS CR, Zitna 25, seminar room, 3rd floor, front building
Chair: David Chodounsky, Bohuslav Balcar

### Ramsey theorem with highly connected homogeneous sets

##### Michael Hrušák
A graph $(\kappa, E)$ is highly homogeneous if all its restrictions on complements of sets of cardinality less than $\kappa$ are homogeneous. We investigate for which cardinals $\theta < \lambda \leq \kappa$ does hold that for every coloring $c:[\kappa]^2\to \theta$ there exists $A$ subset of $\kappa$ of cardinality $\lambda$ and a color $i\in\theta$ such that the graph $(A, c^{-1}(i)\cap [A]^2)$ is highly homogeneous.